Question Number 187607 by SonGoku last updated on 19/Feb/23 $$\: \\ $$$$\:\boldsymbol{\mathrm{Help}}!\:\::\left(\right. \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Should}}\:\:\boldsymbol{\mathrm{i}}\:\:\boldsymbol{\mathrm{partially}}\:\:\boldsymbol{\mathrm{differentiate}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{numerator}}\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{denominator}}? \\ $$$$\: \\ $$$$\:\underset{\left(\boldsymbol{{x}},\:\boldsymbol{\mathrm{y}}\right)\rightarrow\left(\mathrm{0},\mathrm{1}\right)} {\boldsymbol{\mathrm{lim}}}\left[\frac{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:\:+\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:−\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}\right] \\ $$…
Question Number 187598 by horsebrand11 last updated on 19/Feb/23 $$\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{6}}{{x}}−\sqrt{\frac{\mathrm{36}}{{x}^{\mathrm{2}} }+\frac{\mathrm{4}}{{x}}+\mathrm{9}}\:=? \\ $$ Answered by cortano12 last updated on 19/Feb/23 $$\:\:{L}=\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{6}}{{x}}\:−\frac{\mathrm{1}}{{x}}\sqrt{\mathrm{36}+\mathrm{4}{x}+\mathrm{9}{x}^{\mathrm{2}}…
Question Number 56453 by wasim last updated on 16/Mar/19 Commented by wasim last updated on 16/Mar/19 $$\mathrm{please}\:\:\mathrm{solve}\:\mathrm{question}\:\mathrm{7} \\ $$$$ \\ $$$$\mathrm{thanks} \\ $$ Commented by…
Question Number 121958 by bemath last updated on 13/Nov/20 $$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}+\mathrm{cos}\:{x}}{{x}^{\mathrm{3}} \:\mathrm{sin}\:{x}}\:−\:\frac{\mathrm{3}}{{x}^{\mathrm{4}} }\:\right)=? \\ $$$$\:\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{3}^{\mathrm{5}{x}} \:−\:\mathrm{3}^{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}} }{\mathrm{sin}\:\left(\pi{x}\right)}\:=?\: \\ $$ Answered by liberty last…
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Question Number 121822 by liberty last updated on 12/Nov/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}−\mathrm{2cos}\:\mathrm{2x}}}{\mathrm{3}\mid\mathrm{sin}\:\mathrm{4x}\mid}\:=? \\ $$ Answered by bemath last updated on 12/Nov/20 $$\begin{cases}{\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}−\mathrm{2}\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} {x}\right)}}{\mathrm{3}\mid\mathrm{sin}\:\mathrm{4}{x}\mid}\:=\:\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 121813 by bemath last updated on 12/Nov/20 $$\:\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\theta−\theta\:\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\theta}\:=? \\ $$ Answered by bobhans last updated on 12/Nov/20 $$\:\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\theta−\theta\:\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\theta}\:=\: \\ $$$$\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\theta−\frac{\theta^{\mathrm{3}}…